As done in [1]}, to maximize \(g(a,\lambda _L,\lambda _U, \nu )\) , we have to make \(V_{k}-\lambda _L + \lambda _U + \nu {1}=0\) , or otherwise the term \(\inf _{p \in \mathbb {R}^{|\mathcal {Q}|}}\Big [p^T(V_{k}-\lambda _L + \lambda _U + \nu {1})\Big ]\)  will always be \(-\infty \) . Thus, (REF ) becomes:
\(\begin{aligned}\max _{\lambda _L, \lambda _U, \nu } \quad &\sum _{i=1}^{|\mathcal {Q}|}\lambda _{L_i}\check{P}(q,a,q_i) - \sum _{i=1}^{|\mathcal {Q}|}\lambda _{U_i}\hat{P}(q,a,q_i) -\nu \\\mathrm {s.t.:} \quad &\text{ }\lambda _L \succeq 0, \text{ }\lambda _U \succeq 0, \text{ }\nu \in \mathbb {R},\text{ }V_{k}-\lambda _L + \lambda _U + \nu {1}=0\end{aligned}\) 
